residual stresses in strength-mismatched welds and

8/6/2019 Residual Stresses in Strength-mismatched Welds And

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Residual stresses in strength-mismatched welds andimplications on fracture behavior

P. Dong*, J. Zhang

Battelle Memorial Institute, 505 King Avenue, Columbus, OH, 43201-2693, USA

Accepted 27 August 1999

Abstract

The eects of weld strength mismatch on welding residual stresses were discussed based on a series of

recent comprehensive studies. Two typical joint congurations were analyzed in detail: a butt-weldedplate and a multi-pass girth weld. The butt-welded plate represents a severely under-matched weld, in

which repair welding eects were also analyzed. For the girth weld, three weld strength levels were

considered to investigate the weld strength mismatch eects on weld residual stress distributions.

Fracture mechanics analysis was then performed for the multi-pass girth weld for a surface crack

situated along the weld centerline. Welding-induced residual stress elds were assumed to be the

dominant loading mode in all cases. With the dominance of welding-induced residual stress eld, such as

in some of the stress corrosion cracking cases experienced in the utility industry, stress intensity factors

are shown to be an appropriate and convenient fracture mechanics parameter. The implications on

ductile fracture behavior were also discussed in light of the results from this study. # 1999 Elsevier

Science Ltd. All rights reserved.

1. Introduction

Weld metal strength mismatch is referred to as an inhomogeneous strength distribution

across a welded joint resulting from the use of weld metal of either higher or lower strength

than the base material. The former is typically referred to as overmatched and the latter

undermatched. Over the last decade, there has been an increased interest in understanding weld

metal strength mismatch eects on fracture behaviors of welded structures. As a result, a large

Engineering Fracture Mechanics 64 (1999) 485505

0013-7944/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 1 3 - 7 9 4 4 ( 9 9 ) 0 0 0 8 8 - 0

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* Corresponding author. Tel.: +1-614-424-6424; fax: +1-614-424-5263.

E-mail address: [email protected] (P. Dong).


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number of publications on this subject have appeared in the open literature on weld strength

mismatch eects on fracture toughness testing and fracture characterization parameters of

welded structures. Some of the representative work can be found in Refs. [19].

It is known that welding residual stresses can play an important role in the fracture behavior

of welded structures. However, detailed studies on this subject have been scarce in the open

literature. This may have been in part due to the fact that accurate residual stress analyses

require sophisticated numerical tools that have only become available over the last few years.Nonetheless, with prescribed residual stress distributions, Finch and Burdekin conducted nite

element computation of J-integral without weld metal strength mismatch eects [10,11]. Their

results indicated that residual stress eects on J increase steadily as loading increases through

the linear elastic regime. Although intriguing, such results should be interpreted with caution

since the computation of J-integral in its original form no longer possesses the path-

independence property with the presence of weld residual stresses [12]. As a result, appropriate

computational fracture mechanics parameters should be identied or rephrased in order to take

into account the eects of both weld strength mismatch and residual stress [12]. Under residual

stress dominant conditions, stress intensity factor solutions have been used to characterize

quasi-static crack growth behavior in multi-pass girth welds [13,14], where detailed residual

stress states were obtained based on advanced nite element techniques [1518]. Any presence

of weld metal strength mismatch tends to introduce additional complexity in residual stresses,as discussed in Refs. [17,18] for under-matched welds.

In this paper, some of the general residual stress characteristics associated with mismatched

welds are rst discussed using two typical weld congurations. One is a butt-welded plate with

under-matched weld metal. The other is a multi-pass girth weld. For the latter, detailed

residual stress results were given for undermatched, matched, and overmatched conditions.

Fig. 1. AlLi panel specimen with a repair weld.

P. Dong, J. Zhang / Engineering Fracture Mechanics 64 (1999) 485505486


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And nally, the stress intensity factors were computed under the three matching conditions to

study quasi-static crack growth behavior due to the presence of welding-induced residual stress

elds.

2. Residual stresses in a butt-welded plate

Fig. 1 shows an AlLi panel specimen with both initial weld and weld repair. Both advanced

nite element techniques and experimental methods were used to characterize the residual

stress development. Fig. 2 shows the 2D cross-section model (generalized plane-strain

conditions). A special shell element model as shown in Fig. 3 was used to capture some of the

3D residual stress features. A short description of the residual stress analysis procedure is given

below. Detailed discussions on this subject can be found in Refs. [13,1519].

2.1. Analysis procedure

The procedure for welding-induced residual stress analysis can be divided into two parts:

thermal and mechanical analyses. These two analyses are sequentially coupled and thereforecan be carried out in sequence. A thermal analysis solves for the transient temperature eld

associated with the heat ow of welding. The resulting temperature solutions are fed into a

Fig. 2. 2D cross-section model: (a) entire model; (b) fusion prole macrograph and mesh design in weld area.

P. Dong, J. Zhang / Engineering Fracture Mechanics 64 (1999) 485505 487


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mechanical analysis as the thermal driving force for the stress evolution. Residual stresses are

the nal stress state at which all weld passes are completed and the weld is cooled down to the

ambient temperature.For both the thermal and mechanical analyses, temperature-dependent physical and

mechanical properties of the base and ller materials are incorporated. For the AlLi panel

specimen, the room temperature stressstrain curves are given in Fig. 4. The ller metal

strength is signicantly lower than that of the base metal, i.e., a severely undermatched case.

2.2. Initial welds

The shell/plate element model in Fig. 3 was rst used to analyze the residual stress

development for the initial weld. The transverse residual stresses along a line at 7.6 mm from

the weld centerline are shown in Fig. 5. Residual stress measurements (in symbols) were also

obtained with the X-ray diraction technique at four equally spaced positions along this line.It should be noted that the shell/plate element model was only intended to capture some of the

global residual stress characteristics. Nevertheless, the agreement between the measured and

predicted results is reasonable.

Such residual stress distribution characteristics are not completely unexpected. It is well

established that the longitudinal residual stresses are primarily dominated by workpiece's

restraint in the longitudinal direction, and their typical distributions along an initial weld are

illustrated in Fig. 6. The transverse residual stress distribution, however, can be attributed to

both longitudinal and transverse restraints. A simple free-body diagram with an imaginary cut

along the weld centerline is used in Fig. 6 to demonstrate the contribution of weld longitudinal

shrinkage to the variation of the transverse residual stress along the weld as shown in Fig. 5.

Without knowing this important residual stress feature for the transverse component, analysisresults from a 2D model may not be correctly interpreted.

To investigate the detailed local residual stress distributions, the 2D generalized plane strain

element model (see Fig. 3) was used along with prescribed displacement conditions obtained

Fig. 3. Half-panel shell/plate element model.



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from the shell/plate element model, as discussed above. The residual stress results on the top

surface are plotted as a function of distance from the weld centerline in Fig. 7, in which

experimental X-ray diraction measurements are plotted in symbols. The predicted

longitudinal stresses in the weld area (Fig. 7a) clearly indicates the weld metal undermatch

eects (i.e., its yield strength was lower than the base material's by about 45%). The maximum

tensile stress occurs within the HAZ region due to the high yield strength of the base material.

The agreement between the predictions and measurements was considered reasonable,

particularly away from the weld.

The transverse residual stress results on the top surface are shown in Fig. 7b. Within thefusion zone, the transverse component is small. The transverse residual stress reaches its

maximum at the fusion line and is followed by a rapid decrease. Some oscillations can be seen

for some distance further away from the weld before the transverse component gradually

Fig. 4. Room temperature stressstrain curves: (a) initial weld; (b) repair weld.



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approaches zero. It should be noted that clamp positions were located at about 64 mm away

from the weld centerline and that its eects can be clearly seen in the predicted results. The X-

ray diraction measurement results followed the same trend.

Fig. 5. Transverse residual stress distribution along weld length.

Fig. 6. Longitudinal residual stress and corresponding transverse residual stresses due to longitudinal restraint.



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2.3. Repair welds

Once the initial weld residual stress eld was established, as discussed in the previous section,

the repair welding was simulated using the procedures described earlier. The results are also

summarized in Fig. 7. The change in longitudinal residual stresses due to repair is not

Fig. 7. Comparison of nite element predictions and X-ray measurements at panel mid-length: (a) longitudinal

residual stress; (b) transverse residual stress.



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noticeable. However, the transverse residual stress component shows an overall increase,

particularly away from the fusion zone. This trend was further conrmed by the X-ray

measurements, shown in symbols (triangles) in Fig. 7b.

The shell/plate element model was also used to investigate the global features of the repair

weld residual stresses for the entire panel specimen. The resulting transverse residual stress

distribution is given in Fig. 8. High tensile stress occurs within the repaired region and reaches

its maximum at the stop position. Immediately outside the repair weld length (start/stoppositions), the transverse stresses became compressive. X-ray residual stress measurements

conrmed this trend [18]. The detailed results were discussed in Refs. [17,18].

2.4. Cross-section yielding behavior

To investigate the interactions of the repair residual stresses with external loading in such

severely undermatched weld, both the shell element model and wide panel tension specimens

were used. The wide-panel specimens were machined to obtain a at surface within a gauge

length of 508 mm. A thin layer of photo-strain coating was placed onto the specimens over the

gauge length. Tension loading was gradually applied at a specied load increment. Photo-strain

Fig. 8. Transverse residual stress distribution on top surface wide panel specimen (in ksi).



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distribution (maximum shear strain) was obtained in the form of fringe contours on the wide

panel test specimens at each load increment. The nite element results on the wide panel

specimens were processed in the same manner: (1) the total maximum shear strains were

obtained at a given remote loading and (2) the total maximum strains were subtracted by the

total maximum strains due to welding.

Fig. 9. Finite element results maximum shear strains at remote loading of 172 MPa: (a) initial weld; (b) repair

weld.



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Fig. 10. Experimental photostrain results maximum shear strain at remote loading of 172 MPa: (a) initial weld;

(b) repair weld.



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The results in the form of the maximum shear strain (to be consistent with the experimental

photo-strain data) are shown in Fig. 9 at a remote loading level of 172 MPa. The maximum

shear strain distribution for a wide panel specimen only with an initial weld are shown in Fig.

9a. A concentration of fringes as a result of plastic deformation can be seen along the entire

length of the initial weld due to under-matched ller material. The experimental results for

wide panel specimen with an initial weld is given in Fig. 10a. Once a repair weld was

introduced, the maximum shear strain distributions became highly concentrated within therepair weld (Fig. 9b), as conrmed by the experimental photo-strain results in Fig. 10b.

3. Residual stresses in a multi-pass girth weld

Fig. 11 shows the axisymmetric model of a multi-pass girth weld. The inner radius of the

cylinder is 2235 mm and the thickness is 38.1 mm. A layered lumped-pass was used here to

simplify the analysis procedures. A more detailed analysis procedure with 18 passes was used

in Ref. [13] for the same weld. The general residual stress characteristics are essentially the

Fig. 11. Finite element model for a multi-pass girth weld.



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same. The base material is of Type 304 austenitic stainless steel. The mechanical properties are

shown in Table 1. Three ller material strength levels were assumed, i.e., 30% undermatched,

matched, and 30% overmatched with respect to that of base material. In all cases, strain

hardening characteristics were assumed to be the same. The detailed residual stress

development after each passes were shown in detail for the matched case in Ref. [13].

As weld strength mismatch eects are introduced, the magnitude of the transverse residual

stress distributions becomes signicantly dierent, as shown in Fig. 12, although the overallresidual stress distributions share similar characteristics among the three cases. The hoop

residual stress distributions (see Fig. 13), however, become more uniform as the strength of the

weld metal increases, with its change in magnitude being much less noticeable. Figs. 14 and 15

show the detailed comparison of the through-thickness distributions of the axial residual

stresses at the weld centerline, at 12.7 and 22.9 mm from the weld centerline, respectively. Also

shown in Fig. 16 are the axial residual stress distributions on both inner and outer surfaces as

a function of distance from the weld centerline. As expected, the weld metal strength mismatch

eects are most signicant at the weld centerline. The mismatch eects decrease rapidly as the

distance from the weld centerline increases. Outside of heat aected zone (HAZ), the mismatch

eects become negligible for the cases studied.

4. Fracture behavior

To characterize crack behavior within residual stress elds of welded structures, J-integral in

its original formulation may not be conveniently used for nite element computation due to its

path dependency. If residual stresses are dominant near a crack in a component on which

external loading may be negligible, stress intensity factors can be used as a fracture mechanics

parameter to characterize the crack behavior (for detailed discussions on this subject, see Ref.

[12]). An intuitive illustration is given in Fig. 17. Material points such as A and B may be

identied as they undergo welding-induced thermomechanical cycles. Their resulting residual

stress states can be traced to the positions shown with respect to their respective stressstrain

histories during the entire welding process. As the residual stress eld is perturbed, due toeither crack growth or change of external loading, these material points tend to react primarily

with linear response with respect to their residual stress states, as shown in Fig. 17. Within this

context, stress intensity factors can be used as a fracture mechanics parameter, provided

external loading is not dominant.

Table 1

Mechanical properties used for type 304 SS

Young's modulus

(MPa) 103Poisson's ratio Thermal expansion coecient

(1/8C) 106Yield stress

(MPa)

Strain hardening coecient, H

(MPa) 103

2.83 (19.5) 0.27 8.47 (4.7) 36.5 (251.8) 0.44 (3.0)



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4.1. Finite element alternating method

The nite element alternating method (FEAM), which is summarized in Refs. [2023], is the

state of the art method for obtaining stress intensity factors for a 3D surface crack. The major

advantage of the method is that a nite element mesh of the uncracked geometry is all that is

needed to obtain stress intensity factors, displacements, stresses, etc. More importantly, thesame mesh can be used to obtain solutions for many dierent crack sizes (e.g., quasi-static

growing crack) and for multiple cracks. Because the nite element stiness matrix only needs

to be reduced once regardless of the crack size, crack location, crack orientation, crack number

Fig. 12. Transverse (axial) residual stress distributions (in ksi).



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(mixed mode conditions can be handled as well), etc., the method is extremely ecient. The

FEAM methods have been adapted for analyzing a growing crack in residual stress elds [14].

4.2. Stress intensity factor solutions

To investigate the fracture behavior of a small surface crack in the girth weld shown in Fig.11, the residual stress distributions were mapped onto its 3D solid element model as shown in

Fig. 18. As discussed earlier, the FEAM methods only require a conventional 3D solid element

mesh without the need to explicitly model the crack.

Fig. 13. Hoop residual stress distributions in (ksi).



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4.2.1. Matched weld

The stress intensity factor solutions (KI) along the crack front are shown in Fig. 18 for four

values of the crack depth (a2) for the matched case. With an initial crack size of a1=88.9 mm

and a2=5.1 mm, the stress intensity factor reaches its maximum at the deepest position

Fig. 14. Through-thickness axial residual stress distributions at weld centerline.

Fig. 15. Through-thickness axial residual stress distributions.



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(elliptical angle of 908). As the crack depth is increased to a2=7.6 mm, an approximatelyuniform increase in stress intensity factors can be seen along the crack front. It is interesting to

note that the axial residual stress before a crack is introduced varies from highly tensile to

compressive at a depth of about 5.1 mm from the inner surface (see Fig. 14). However, as the

Fig. 16. Axial residual stress distributions on inner and outer surfaces.

Fig. 17. Illustration of material points (A and B) before and after perturbation with respect to their residual stress

states.



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crack grows deeper, for instance after a2=10.2 mm, the stress intensity factor at the deepest

position decreases rapidly and the maximum value occurs at about 228 from the surface. A

similar behavior was also seen in a number of other pipe girth welds [14].

4.2.2. Mismatched welds

With the residual stress states obtained under 30% undermatched and 30% overmatched

Fig. 18. Stress intensity factors (K) for elliptical surface cracks matched case (alternating nite element method).



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Fig. 19. Comparison of stress intensity factor solutions mismatched cases.



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weld strengths, an identical FEAM procedure was repeated to compute the stress intensity

factor solutions. The results are summarized in Fig. 19 for an elliptical surface crack with two

representative depths. At a2=5.1 mm, the overmatched case gives a higher stress intensity

factor value along the crack front than that of the matched case (short dashed lines). The

undermatched case shows a signicant reduction of the stress intensity factor values from the

matched case, more than 60% at the deepest position. As the crack grows deeper, for instance

at a2=10.2 mm, the dierence between the overmatched and matched cases becomes smallerwhile the reduction in KI for the undermatched cases remains signicant.

5. Closure

Without considering weld residual stresses, weld strength mismatch eects become noticeable

only if the plastic zone at the crack tip starts to interact with base material [58]. This typically

requires a load level that is suciently high. Once welding-induced residual stresses are

considered, weld metal strength mismatch can aect the fracture behavior of welded structures

for the entire loading spectrum. Often, fracture behavior at the lower end of the loading

spectrum is of a particular concern if there exist possibilities of brittle fracture. At the lowerend of the loading spectrum, weld residual stresses could act as a sole driving force for crack

growth, e.g., as shown for some of the stress corrosion cracking cases [14]. Obviously, the weld

residual stresses are strongly dependent on the weld metal mismatch conditions, as illustrated

in this paper. At the upper end of the loading spectrum, it is typically assumed that the eects

of the weld residual stresses should be insignicant. However, the presence of high residual

stresses at an early loading stage could signicantly alter the plastic zone development at a

crack tip or even set o a dierent cross-section yielding mechanisms at a later stage of the

loading, as illustrated in Ref. [18] on repair welded wide panel specimens.

Therefore, the combined eects of the strength mismatch and residual stresses on the

fracture behavior should be of critical importance in fracture mechanics analysis of welded

structures. Today's research activities in the area of weld strength mismatch should beexpanded to address weld residual stress eects. The results from the present study can serve as

a basis for a coordinated systematic investigation on this subject. Specically, the following

observations from this investigation may provide an impetus for such an endeavor.

1. The development of weld residual stresses can be complex and is strongly dependent on,

among other things, joint conguration and welding procedures. As advanced

computational modeling techniques have become available over the recent years, detailed

residual stress information incorporating weld strength mismatch eects can be readily

obtained for the purpose of fracture mechanics analysis of welded structures.

2. Weld strength mismatch eects tend to be conned to a small region encompassing the

weld. Although their overall residual stress distributions are rather similar to the matched

weld, the magnitude of the transverse residual stress component can be signicantlyincreased in overmatched welds and decreased in undermatched welds. However, the

increase in magnitude for the hoop or longitudinal residual stresses is much less noticeable.

3. It seems that undermatched welds can oer a signicant less fracture driving force if the



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residual stresses are a dominant loading mode. If the large scale plastic deformation occurs

prior to nal failure under dominant external loading conditions, the residual stresses in

undermatched welds can be sucient to trigger an unfavorable cross-section yielding mode,

as discussed for the repair weld case.

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